America’s top military officer said Russia bears ultimate responsibility for an airstrike on a U.N. humanitarian convoy in Syria, and that he does not favor sharing military intelligence with Moscow in the Syrian conflict.

“Two Russian aircraft were in that area at that time [when the convoy was attacked],” said General Joseph Dunford, chairman of the Joint Chiefs of Staff, testifying Thursday before the Senate Armed Services Committee.

“I can’t conclusively say it was the Russians, but it was either the Russians or the regime [of Syrian President Bashar al-Assad],” Dunford said, adding that, either way, “the Russians are responsible” for Monday's deadly attack near Aleppo that destroyed 18 trucks. Syria and Russia have denied any role in the attack.

As for the coordinated efforts between the United States and Russia envisioned in a failed Syrian cease-fire, Dunford said, “I do not believe it would be a good idea to share intelligence with the Russians.”

WATCH: General Dunford's statement on intelligence sharing with Russia

“Nowhere is America’s strategic drift clearer than in Syria,” McCain said. “After more than 400,000 dead and half the population driven from their homes … the administration still has no plausible vision of an end-state for Syria.

“Instead … President Obama sent his intrepid but delusional secretary of state [John Kerry] to tilt yet again at the windmill of cooperating with Vladimir Putin,” the senator added.

Secretary Carter insisted progress is being made against Islamic State in both Syria and Iraq.

“We’re putting ISIL on the path to a lasting defeat in Iraq and Syria – particularly as we embark on a decisive phase of our campaign, to collapse ISIL’s control of Raqqa [Syria] and Mosul [Iraq],” Carter said, using an acronym for Islamic State, in what could be his final appearance before the committee as a member of Obama’s national security team.

General Dunford concurred, saying, “We are succeeding in that campaign.” But he conceded that a core U.S. goal, the departure of Syrian President Bashar al-Assad, is unlikely to be met in the near future.

The hearing was held at a time when Congress is struggling to agree on a budget to keep the U.S. government funded, including the Pentagon. Carter concurred with McCain and others in saying that the military is best served by a reliable annual appropriation rather than the short-term spending extension currently being crafted by lawmakers.